Zero-free self-contained computing system

A zero-free self-contained computing system, comprising:

• a. a processing core including
• i. a modular arithmetic unit configured to perform arithmetic operations using a zero free digit set;
• ii. a fractal digital root encoder configured to generate iterative root of sum representations according to a recurrence rule;
• and
• iii. an oscillatory number system controller comprising logic circuitry configured to regulate transitions between representational states using an oscillatory modular update cycle;
• b. a memory architecture including
• i. a zero free cache encoding module comprising memory mapping logic configured to store values using a zero free positional representation;
• and
• ii. a self correcting address mapping module comprising address translation logic configured to detect representational inconsistencies and remap addresses using a correction rule;
• and
• c. a logic controller including
• i. a zero free instruction processing unit comprising decoding logic configured to interpret zero free opcodes and execution logic configured to process operands represented using the zero free digit set;
• and
• ii. a unified integer and floating point framework configured to process numerical values using a common zero free representational basis.